Apr 30, 2024

numbers are crazy

math ventures #2

This is a part of my ongoing series of math ventures.

It's been almost a week since I posted my last update.

For the context: #

I have been studying Serge Lang's Basic Mathematics with the help of Real Physics' lectures to up my "game" in maths. I want to revisit the fundamentals and develop a better foundation.
I am hoping to finish the book by the end of June. I haven't "grinded" textbooks this way before, but I know that this is going to be a great experience.

Wisdom gained from Math #

I finished the first chapter of Basic Mathematics called "Numbers". One thing to keep in mind that I didn't study everyday, which clarifies why it took almost a WEEK.

Nevertheless, it was a good revision to the fundamental rules of working with numbers, how we use operators and few interesting proofs. One interesting thing it taught me is how one can use logic to prove stuff. That reasoning is necessary when you're working with higher math. As,

"Math builds upon itself."

It's like a pyramid, you can think of it that way. Most of the things that are taught at a lower level comes handy in a higher one. You need that "prerequisite" knowledge in order to excel at it. For example, you need to know how to work with fractions in order to solve this equation:

And you'd need to know how to solve that equation to solve this equation:

...and so on. Right? Yes. It is a ladder you can climb.

One can also say that knowledge builds upon itself, but iff (that's a math term, for "if and only if") one is able to connect it appropriately. It depends on the persons capacity. Polymaths are adept in connecting different fields, and thus, excel at many.

What's in this chapter? #

This chapter, though named "Numbers", doesn't only talk about Arithmetic, but also Algebra, mostly Algebra. In fact, it is under Part 1: Algebra of the book.

You learn about:

• Integers, Number Line; basic revision stuff
• Rules of Operations and neat proofs
• Basic Number Theory: divisibility, even odd, exponents
• Brief on Rational Numbers
• Few new terms like factorial, binomial coefficient, inverses, etc.

That is the core of this chapter. The exercises include a lot of intuitive problems, where you have to stretch the domain your brain works in. You'll have to try using that logical side instead of the "brute" side, and by that I mean doing math efficiently.

Of course, you'll have to solve some problems by hit-and-trial, and that's fun too! You'll also have to use your calculator quite a bit; especially when you get to the exponential decay type questions which involves problems like:

I thought those problems were really interesting. At one moment, I thought I actually crashed my calculator (on a livestream!):

Anyway, I learned how to use another function of my calculator, which is really exciting. What's more exciting is the next chapters! I can't wait to grit through this. Of course, it's sometimes painful (the only thing I am masochistic about: knowledge), yet I am glad that I am doing this.

See ya on the next update.

P.S: Pretty glad on adding MathJax here hehe.

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